In this paper we analyze
the performance of Warning Propagation, a popular message
passing algorithm. We show that for 3CNF formulas drawn from a certain
distribution over random satisfiable 3CNF formulas, commonly
referred to as the planted-assignment distribution, running
Warning Propagation in the standard way (run message
passing until convergence, simplify the formula according to the
resulting assignment, and satisfy the remaining subformula, if
necessary, using a simple “off the shelf” heuristic)
works when the clause-variable ratio is a sufficiently large constant.
We are not aware of previous rigorous analysis showing the effectiveness
of message passing algorithms for satisfiability instances.